What is the extraneous solution to these equations? $\dfrac{x^2 - 11x}{x - 4} = \dfrac{x - 32}{x - 4}$
Explanation: Multiply both sides by $x - 4$ $ \dfrac{x^2 - 11x}{x - 4} (x - 4) = \dfrac{x - 32}{x - 4} (x - 4)$ $ x^2 - 11x = x - 32$ Subtract $x - 32$ from both sides: $ x^2 - 11x - (x - 32) = x - 32 - (x - 32)$ $ x^2 - 11x - x + 32 = 0$ $ x^2 - 12x + 32 = 0$ Factor the expression: $ (x - 8)(x - 4) = 0$ Therefore $x = 8$ or $x = 4$ At $x = 4$ , the denominator of the original expression is 0. Since the expression is undefined at $x = 4$, it is an extraneous solution.